Mapping Multiple Distances in a Multidomain Protein for the Identification of Folding Intermediates

The investigation and understanding of the folding mechanism of multidomain proteins is still a challenge in structural biology. The use of single-molecule Förster resonance energy transfer offers a unique tool to map conformational changes within the protein structure. Here, we present a study following denaturant-induced unfolding transitions of yeast phosphoglycerate kinase by mapping several inter- and intradomain distances of this two-domain protein, exhibiting a quite heterogeneous behavior. On the one hand, the development of the interdomain distance during the unfolding transition suggests a classical two-state unfolding behavior. On the other hand, the behavior of some intradomain distances indicates the formation of a compact and transient molten globule intermediate state. Furthermore, different intradomain distances measured within the same domain show pronounced differences in their unfolding behavior, underlining the fact that the choice of dye attachment positions within the polypeptide chain has a substantial impact on which unfolding properties are observed by single-molecule Förster resonance energy transfer measurements. Our results suggest that, to fully characterize the complex folding and unfolding mechanism of multidomain proteins, it is necessary to monitor multiple intra- and interdomain distances because a single reporter can lead to a misleading, partial, or oversimplified interpretation.     

Relating Single-Molecule Measurements to Thermodynamics

Measurements made on large ensembles of molecules are routinely interpreted using thermodynamics, but the normal rules of thermodynamics may not apply to measurements made on single molecules. Using a polymer stretching experiment as an example, it is shown that in the limit of a single, short molecule the outcome of experimental measurements may depend on which variables are held fixed and which are allowed to fluctuate. Thus an experiment in which the end-to-end distance of the polymer molecule is fixed and the tension fluctuates yields a different result than an experiment where the force is fixed and the end-to-end distance fluctuates. It is further shown that this difference is due to asymmetry in the distribution of end-to-end distances for a single molecule, and that the difference vanishes in the appropriate thermodynamic limit; that is, as the polymer molecule becomes long compared to its persistence length. Despite these differences, much of the thermodynamic formalism still applies on the single-molecule level if the thermodynamic free energies are replaced with appropriate potentials of mean force. The primary remaining differences are consequences of the fact that unlike the free energies, the potentials of mean force are not in general homogeneous functions of their variables. The basic thermodynamic concepts of an intensive or extensive quantity, and the thermodynamic relationships that follow from them, are therefore less useful for interpreting single-molecule experiments.     

Genetic Distances Based on Quantitative Traits

Morphological data showing continuous distributions, polygenically controlled, may be particularly useful in intergroup classification below the species level; an appropriate distance analysis based on these traits is an important tool in evolutionary biology and in plant and animal breeding.--The interpretation of morphological distances in genetic terms is not easy because simple phenotypic data may lead to biased estimates of genetic distances. Convenient estimates can be obtained whenever it is possible to breed populations according to a suitable crossing design and to derive information from genetic parameters.--A general method for determining genetic distances is proposed. The procedure of multivariate analysis of variance is extended to estimate appropriate genetic parameters (genetic effects). Not only are optimal statistical estimates of parameters obtained but also the procedure allows the measurement of genetic distances between populations as linear functions of the estimated parameters, providing an appropriate distance matrix that can be defined in terms of these parameters. The use of the T2 statistic, defined in terms of the vector of contrasts specifying the distance, permits the testing of the significance of any distance between any pair of populations that may be of interest from a genetic point of view.--A numerical example from maize diallel data is reported in order to illustrate the procedure. In particular, heterosis effects are used as the basis for estimates of genetic divergence between populations.     

Mining biochemical information: lessons taught by the ribosome

The publication of the crystal structures of the ribosome offers an opportunity to retrospectively evaluate the information content of hundreds of qualitative biochemical and biophysical studies of these structures. We assessed the correspondence between more than 2,500 experimental proximity measurements and the distances observed in the ribosomal crystals. Although detailed experimental procedures and protocols are unique in almost each analyzed paper, the data can be grouped into subsets with similar patterns and analyzed in an integrative fashion. We found that, for crosslinking, footprinting, and cleavage data, the corresponding distances observed in crystal structures generally did not exceed the maximum values expected (from the estimated length of the agent and maximal anticipated deviations from the conformations found in crystals). However, the distribution of distances had heavier tails than those typically assumed when building three-dimensional models, and the fraction of incompatible distances was greater than expected. Some of these incompatibilities can be attributed to the experimental methods used. In addition, the accuracy of these procedures appears to be sensitive to the different reactivities, flexibilities, and interactions among the components. These findings demonstrate the necessity of a very careful analysis of data used for structural modeling and consideration of all possible parameters that could potentially influence the quality of measurements. We conclude that experimental proximity measurements can provide useful distance information for structural modeling, but with a broad distribution of inferred distance ranges. We also conclude that development of automated modeling approaches would benefit from better annotations of experimental data for detection and interpretation of their significance.     

DISTANCE METHODS: A REPLY TO FARRIS

Abstract— Farris (1985) claimed that my assertions about unbiasedness and consistency of estimates of a phylogeny obtained by least squares fitting are in error. The counterexample he constructed violates the assumptions of additivity and independence of distances which were clearly stated in my earlier paper. As such it is not a valid counterexample. It is argued, contrary to Farris's claims, that one need not avoid nonmetric distances, and that one should avoid negative branch lengths in estimates of phylogenies from distance data. Statistical tests of clockness, and, to a limited extent, of alternative phylogenies can be constructed, and these are demonstrated by example. A computer program to infer phylogenies from distance matrices has been in free distribution by me for several years; it seems as effective as the program recently announced by Farris. Information on phylogenies is present in distance data, as in other kinds of data, and statistical methods can be developed to extract it.     

Distances between the antigen-binding sites of three murine antibody subclasses measured using neutron and X-ray scattering.

For three different murine immunoglobulins (IgG subclasses 1, 2a, and 2b), the distances between their antigen-binding sites have been measured using neutron scattering from deuterated antigens complexed with proteated IgG. Neutron-scattering data were measured for each antibody-antigen complex in a 41% D2O solvent. Unlike the proteated antibody molecule, the deuterated antigens are strongly contrasted against the 41% D2O solvent and give rise to a scattering profile that contains an interference term related to the distance between the deuterated antigens. For all three subclasses, the damping of this interference term, which gives information on the relative flexibility of the antigen-binding sites, indicates that a single distance is inadequate to describe the observed scattering and a distribution of distances is needed. The scattering profile has been modeled for each subclass to give the mean distance between the antigens and the variance of this distance. For all three IgG subclasses, the mean distance is between 117 and 134 A, and the variance is large (approximately 40 A), indicating a high degree of flexibility of the Fab arms. Small-angle X-ray scattering measurements on the same samples are consistent with the neutron-scattering results.     

Structure, dynamics, and branch migration of a DNA Holliday junction: a single-molecule fluorescence and modeling study

The Holliday junction (HJ) is a central intermediate of various genetic processes, including homologous and site-specific DNA recombination and DNA replication. Elucidating the structure and dynamics of HJs provides the basis for understanding the molecular mechanisms of these genetic processes. Our previous single-molecule fluorescence studies led to a model according to which branch migration is a stepwise process consisting of consecutive migration and folding steps. These data led us to the conclusion that one hop can be more than 1 basepair (bp); moreover, we hypothesized that continuous runs over the entire sequence homology (5 bp) can occur. Direct measurements of the dependence of the fluorescence resonance energy transfer (FRET) value on the donor-acceptor (D-A) distance are required to justify this model and are the major goal of this article. To accomplish this goal, we performed single-molecule FRET experiments with a set of six immobile HJ molecules with varying numbers of bps between fluorescent dyes placed on opposite arms. The designs were made in such a way that the distances between the donor and acceptor were equal to the distances between the dyes formed upon 1-bp migration hops of a HJ having 10-bp homology. Using these designs, we confirmed our previous hypothesis that the migration of the junction can be measured with bp accuracy. Moreover, the FRET values determined for each acceptor-donor separation corresponded very well to the values for the steps on the FRET time trajectories, suggesting that each step corresponds to the migration of the branch at a defined depth. We used the dependence of the FRET value on the D-A distance to measure directly the size for each step on the FRET time trajectories. These data showed that one hop is not necessarily 1 bp. The junction is able to migrate over several bps, detected as one hop and confirming our model. The D-A distances extracted from the FRET properties of the immobile junctions formed the basis for modeling the HJ structures. The composite data fit a partially opened, side-by-side model with adjacent double-helical arms slightly kinked at the four-way junction and the junction as a whole adopting a global X-shaped form that mimics the coaxially stacked-X structure implicated in previous solution studies.     

Statistical interpretation of fluorescence energy transfer measurements in macromolecular systems.

A statistical method is presented for the interpretation of intramolecular distance measurements by the fluorescence energy transfer technique in systems for which the detailed geometries of the donor-acceptor pairs are unknown. This method enables calculation of the probability that a specified distance range corresponds to the actual distance to be measured. It makes use of the numerically calculated probability density function for the distance of interest. The two general systems considered are the single donor-acceptor pair and the multi-donor-single-acceptor transfer. In both systems, the statistical method incorporates the uncertainty in the orientation of the donor and acceptor dipoles. In addition, it can take into account the rotational mobility of the donor dipoles determined by time-dependent emission anisotropy measurements. When more than one donor is involved in the transfer process, the uncertainties associated with the number and location of individual donors and the size and shape of the donor distribution are also incorporated in calculating the distance ranges. Application of the method was demonstrated for a wide range of transfer efficiency and Ro values for the single donor-acceptor system. Specific examples are also presented for interpretation of both single donor-acceptor and multi-donor-single-acceptor energy transfer measurements performed in order to reveal the spatial relationship of the sigma subunit and the rifampicin binding site in the Escherichia coli RNA polymerase (see Wu, C.-W., Yarbrough, L. R., Wu, F. Y.-H., and Hillel, Z. (1976), Biochemistry, preceding paper in this issue). Analysis of these energy transfer data by methods which use average values of the unknown geometrical parameters of the system yielded results similar to those obtained by the statistical method. However, the statistical method represents a more realistic approach to the interpretation of energy transfer measurements since it provides information concerning the entire range of possible distances and their relative likelihood.     

Relationship between 17 Venezuelan counties estimated through communality of surnames

The coefficients of relationship and the Euclidean distances between 17 Venezuelan counties were estimated based on the frequency distribution of surnames obtained from the 1984 Venezuelan register of electors. In general, the coefficients of relationship between counties within the same state were higher than those between counties from different states. Euclidean distances exhibited the opposite relationship. Spearman's correlation coefficients for 136 pairs of counties were estimated between geographic and Euclidean distances (r = 0.41), geographic distance and coefficient of relationship (r = -0.44) and between Euclidean distance and coefficient of relationship (r = -0.48). The effect of partial geographic isolation on the frequency distribution of surnames is shown in the State of Falcón, where an isthmus separates two counties of the peninsula from two others on the mainland, and in Mérida, where the Venezuelan Andes separates three counties from the rest of the country. Our results suggest that Euclidean distances are less influenced by common surnames than the coefficients of relationship. They also indicate that in Venezuela a high proportion of the population has remained sedentary until recently, and this gives rise to the focal distribution of some surnames.     

Optimization of cell morphology measurement via single-molecule tracking PALM

In neurons, the shape of dendritic spines relates to synapse function, which is rapidly altered during experience-dependent neural plasticity. The small size of spines makes detailed measurement of their morphology in living cells best suited to super-resolution imaging techniques. The distribution of molecular positions mapped via live-cell Photoactivated Localization Microscopy (PALM) is a powerful approach, but molecular motion complicates this analysis and can degrade overall resolution of the morphological reconstruction. Nevertheless, the motion is of additional interest because tracking single molecules provides diffusion coefficients, bound fraction, and other key functional parameters. We used Monte Carlo simulations to examine features of single-molecule tracking of practical utility for the simultaneous determination of cell morphology. We find that the accuracy of determining both distance and angle of motion depend heavily on the precision with which molecules are localized. Strikingly, diffusion within a bounded region resulted in an inward bias of localizations away from the edges, inaccurately reflecting the region structure. This inward bias additionally resulted in a counterintuitive reduction of measured diffusion coefficient for fast-moving molecules; this effect was accentuated by the long camera exposures typically used in single-molecule tracking. Thus, accurate determination of cell morphology from rapidly moving molecules requires the use of short integration times within each image to minimize artifacts caused by motion during image acquisition. Sequential imaging of neuronal processes using excitation pulses of either 2 ms or 10 ms within imaging frames confirmed this: processes appeared erroneously thinner when imaged using the longer excitation pulse. Using this pulsed excitation approach, we show that PALM can be used to image spine and spine neck morphology in living neurons. These results clarify a number of issues involved in interpretation of single-molecule data in living cells and provide a method to minimize artifacts in single-molecule experiments.     

Error distribution derived NOE distance restraints

Errors and imprecisions in distance restraints derived from NOESY peak volumes are usually accounted for by generous lower and upper bounds on the distances. In this paper, we propose a new form of distance restraints, replacing the subjective bounds by a potential function obtained from the error distribution of the distances. We derived the shape of the potential from molecular dynamics calculations and by comparison of NMR data with X-ray crystal structures. We used complete cross-validation to derive the optimal weight for the data in the calculation. In a model system with synthetic restraints, the accuracy of the structures improved significantly compared to calculations with the usual form of restraints. For experimental data sets, the structures systematically approach the X-ray crystal structures of the same protein. Also standard quality indicators improve compared to standard calculations. The results did not depend critically on the exact shape of the potential. The new approach is less subjective and uses fewer assumptions in the interpretation of NOESY peak volumes as distance restraints than the usual approach. Figures of merit for the structures, such as the RMS difference from the average structure or the RMS difference from the data, are therefore less biased and more meaningful measures of structure quality than with the usual form of restraints.     

DISTANCE DATA REVISITED

Abstract— Objections to my earlier demonstration, that the branch lengths of trees fitted to distance matrices have no physical interpretation, are shown to be ill-founded. In particular the contention of Felsenstein, that fitted lengths estimate expectations of amounts of change, is shown to lead to a paradox. A method is introduced for constructing multiple trees of optimal or near-optimal fit to distance data, and this is found to give better performance than previous methods. Most published trees based on distances have been poorly chosen. Consensus trees of several trees with near-optimal fit are found to be quite poorly resolved, and it appears that molecular distances seldom provide much useful information on phylogenetic relationships.     

Fluorescence Quenching by TEMPO: A Sub-30 Å Single-Molecule Ruler

A series of DNA molecules labeled with 5-carboxytetramethylrhodamine (5-TAMRA) and the small nitroxide radical TEMPO were synthesized and tested to investigate whether the intramolecular quenching efficiency can be used to measure short intramolecular distances in small ensemble and single-molecule experiments. In combination with distance calculations using molecular mechanics modeling, the experimental results from steady-state ensemble fluorescence and fluorescence correlation spectroscopy measurements both show an exponential decrease in the quenching rate constant with the dye-quencher distance in the 10-30 Å range. The results demonstrate that TEMPO-5-TAMRA fluorescence quenching is a promising method to measure short distance changes within single biomolecules.     

The Teaching of “Adaptation”

The use of the data from various athletic sports for exercises in the interpretation of data is proposed, and accounts are given of two such exercises. The first looks at the relationship between time and distance in world records for men running. When the logarithm of the time is plotted against the logarithm of the distance a straight line is produced. Thefactors that govern the speeds at which various distances are run are discussed and the application of these to other sports and to animals other than man is briefly mentioned. The second exercise looks at anomalous performances by men running in the 1968 Olympic Games which took place at high altitude. It is shown that while the lowered air resistance increased the speeds in sprint events, and the lowered oxygen content slowed down speeds in long distance events, these were not the only factors involved in limiting speeds.

Among the advantages of the use of such data are that they are readily and easily available, that they are the result of a lengthy selection process involving many subjects, that they appeal to students interested in sport and that they can link courses in biology and physical education.     

Orientation factor in steady-state and time-resolved resonance energy transfer measurements.

Resonance energy transfer measurements provide a way to estimate distances between chromophores attached to different sites of macromolecules. There are two unknowns involved in resonance energy transfer measurements, the distance between two chromophores and their relative orientation. When static orientational disorder exists, the orientation factor, kappa 2, can vary from 0 to 4, leading to considerable uncertainty in estimation of distances. Fluorescence polarization anisotropy measurements can reduce the degree of uncertainty [Dale & Eisinger (1974) Biopolymers 13, 1573]. There may still be substantial error bounds for the average distance measurements. Time-resolved fluorescence measurements provide an "apparent" average distance and distance distribution containing contributions by both distance and orientation. The contribution of orientation to observed "apparent" average distance and distance distribution widths has been estimated for both simulated and real data. With a single unique distance as input in the simulation and with random but static orientation of donor and acceptor, the recovered average distance is very close to that of the input when the input distance is close to or larger than the F?rster distance. The recovered width of apparent distance distribution can be substantial and it changes as a function of F?rster distance to average distance ratio and as a function of F?rster distance. Similar conclusions apply to the case where there is a real distance distribution. Motional averaging of the orientation was simulated by the Monte Carlo method to estimate the contribution of orientation when chromophores have certain degrees of mobility.(ABSTRACT TRUNCATED AT 250 WORDS)     

Single-molecule fluorescence resonance energy transfer

Fluorescent resonance energy transfer (FRET) is a powerful technique for studying conformational distribution and dynamics of biological molecules. Some conformational changes are difficult to synchronize or too rare to detect using ensemble FRET. FRET, detected at the single-molecule level, opens up new opportunities to probe the detailed kinetics of structural changes without the need for synchronization. Here, we discuss practical considerations for its implementation including experimental apparatus, fluorescent probe selection, surface immobilization, single-molecule FRET analysis schemes, and interpretation.     

Structural changes of yellow Cameleon domains observed by quantitative FRET analysis and polarized fluorescence correlation spectroscopy

Förster resonance energy transfer (FRET) is a widely used method for monitoring interactions between or within biological macromolecules conjugated with suitable donor-acceptor pairs. Donor fluorescence lifetimes in absence and presence of acceptor molecules are often measured for the observation of FRET. However, these lifetimes may originate from interacting and noninteracting molecules, which hampers quantitative interpretation of FRET data. We describe a methodology for the detection of FRET that monitors the rise time of acceptor fluorescence on donor excitation thereby detecting only those molecules undergoing FRET. The large advantage of this method, as compared to donor fluorescence quenching method used more commonly, is that the transfer rate of FRET can be determined accurately even in cases where the FRET efficiencies approach 100% yielding highly quenched donor fluorescence. Subsequently, the relative orientation between donor and acceptor chromophores is obtained from time-dependent fluorescence anisotropy measurements carried out under identical conditions of donor excitation and acceptor detection. The FRET based calcium sensor Yellow Cameleon 3.60 (YC3.60) was used because it changes its conformation on calcium binding, thereby increasing the FRET efficiency. After mapping distances and orientation angles between the FRET moieties in YC3.60, cartoon models of this FRET sensor with and without calcium could be created. Independent support for these representations came from experiments where the hydrodynamic properties of YC3.60 under ensemble and single-molecule conditions on selective excitation of the acceptor were determined. From rotational diffusion times as found by fluorescence correlation spectroscopy and consistently by fluorescence anisotropy decay analysis it could be concluded that the open structure (without calcium) is flexible as opposed to the rather rigid closed conformation. The combination of two independent methods gives consistent results and presents a rapid and specific methodology to analyze structural and dynamical changes in a protein on ligand binding.     

Accommodating unmodeled heterogeneity in double-observer distance sampling surveys

Mark-recapture models applied to double-observer distance sampling data neglect the information on relative detectability of objects contained in the distribution of observed distances. A difference between the observed distribution and that predicted by the mark-recapture model is symptomatic of a failure of the assumption of zero correlation between detection probabilities implicit in the mark-recapture model. We develop a mark-recapture-based model that uses the observed distribution to relax this assumption to zero correlation at only one distance. We demonstrate its usefulness in coping with unmodeled heterogeneity using data from an aerial survey of crabeater seals in the Antarctic.